mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 02:02:39 +08:00
Dave Marchant
213 lines
9.2 KiB
Python
213 lines
9.2 KiB
Python
from scipy.sparse import linalg
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from scipy import sparse
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from sputils import *
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from utils import *
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from sputils import *
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from numpy import *
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from getEdgeTangent import *
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from inv3X3BlockDiagonal import *
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from getCellVolume import getCellVolume
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def subarray(T, i1, i2, i3):
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return take(take(take(T, i1, 0), i2, 1), i3, 2)
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def getEdgeInnerProduct(X, Y, Z, sigma):
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"""A = getEdgeInnerProduct(X, Y, Z, sigma)
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node(i,j,k+1) ------ edge2(i,j,k+1) ----- node(i,j+1,k+1)
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/ /
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/ / |
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edge3(i,j,k) face1(i,j,k) edge3(i,j+1,k)
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/ / |
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/ / |
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node(i,j,k) ------ edge2(i,j,k) ----- node(i,j+1,k)
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| | node(i+1,j+1,k+1)
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edge1(i,j,k) face3(i,j,k) edge1(i,j+1,k)
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node(i+1,j,k) ------ edge2(i+1,j,k) ----- node(i+1,j+1,k)
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no | node | e1 | e2 | e3
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000 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k
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100 | i+1,j ,k | i ,j ,k | i+1,j ,k | i+1,j ,k
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010 | i ,j+1,k | i ,j+1,k | i ,j ,k | i ,j+1,k
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110 | i+1,j+1,k | i ,j+1,k | i+1,j ,k | i+1,j+1,k
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001 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k
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101 | i+1,j ,k+1 | i ,j ,k+1 | i+1,j ,k+1 | i+1,j ,k
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011 | i ,j+1,k+1 | i ,j+1,k+1 | i ,j ,k+1 | i ,j+1,k
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111 | i+1,j+1,k+1 | i ,j+1,k+1 | i+1,j ,k+1 | i+1,j+1,k
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"""
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m = array(shape(X))-1
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nc = prod(m)
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me1 = m + array([0, 1, 1]); ne1 = prod(me1)
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me2 = m + array([1, 0, 1]); ne2 = prod(me2)
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me3 = m + array([1, 1, 0]); ne3 = prod(me3)
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e1x,e1y,e1z,e2x,e2y,e2z,e3x,e3y,e3z,norme1,norme2,norme3 = getEdgeTangent(X,Y,Z)
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i = int64(linspace(0,m[0]-1,m[0]))
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j = int64(linspace(0,m[1]-1,m[1]))
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k = int64(linspace(0,m[2]-1,m[2]))
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ii,jj,kk = ndgrid(i,j,k)
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ii = mkvc(ii); jj = mkvc(jj); kk = mkvc(kk)
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## --------
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# no | node | e1 | e2 | e3
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# 000 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k
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ind1 = sub2ind(me1,hstack3(ii,jj,kk))
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ind2 = sub2ind(me2,hstack3(ii,jj,kk)) + ne1
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ind3 = sub2ind(me3,hstack3(ii,jj,kk)) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P000 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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invT000 = inv3X3BlockDiagonal(subarray(e1x,i,j,k) , subarray(e1y,i,j,k), subarray(e1z,i,j,k),
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subarray(e2x,i,j,k) , subarray(e2y,i,j,k), subarray(e2z,i,j,k) ,
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subarray(e3x,i,j,k) , subarray(e3y,i,j,k), subarray(e3z,i,j,k) )
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## --------
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# no | node | e1 | e2 | e3
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# 100 | i+1,j ,k | i ,j ,k | i+1,j ,k | i+1,j ,k
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ind1 = sub2ind(me1,hstack3(ii,jj,kk))
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ind2 = sub2ind(me2,hstack3(ii+1,jj,kk)) + ne1
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ind3 = sub2ind(me3,hstack3(ii+1,jj,kk)) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P100 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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invT100 = inv3X3BlockDiagonal(subarray(e1x,i,j,k), subarray(e1y,i,j,k), subarray(e1z,i,j,k),
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subarray(e2x,i+1,j,k), subarray(e2y,i+1,j,k), subarray(e2z,i+1,j,k),
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subarray(e3x,i+1,j,k) , subarray(e3y,i+1,j,k), subarray(e3z,i+1,j,k))
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## --------
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# no | node | e1 | e2 | e3
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# 010 | i ,j+1,k | i ,j+1,k | i ,j ,k | i ,j+1,k
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ind1 = sub2ind(me1,hstack3(ii,jj+1,kk))
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ind2 = sub2ind(me2,hstack3(ii,jj,kk)) + ne1
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ind3 = sub2ind(me3,hstack3(ii,jj+1,kk)) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P010 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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invT010 = inv3X3BlockDiagonal(subarray(e1x,i,j+1,k) , subarray(e1y,i,j+1,k) , subarray(e1z,i,j+1,k) ,
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subarray(e2x,i,j,k) , subarray(e2y,i,j,k) , subarray(e2z,i,j,k) ,
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subarray(e3x,i,j+1,k) , subarray(e3y,i,j+1,k) ,subarray( e3z,i,j+1,k) )
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## --------
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# no | node | e1 | e2 | e3
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# 110 | i+1,j+1,k | i ,j+1,k | i+1,j ,k | i+1,j+1,k
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ind1 = sub2ind(me1,hstack3(ii,jj+1,kk))
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ind2 = sub2ind(me2,hstack3(ii+1,jj,kk)) + ne1
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ind3 = sub2ind(me3,hstack3(ii+1,jj+1,kk)) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P110 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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invT110 = inv3X3BlockDiagonal(subarray(e1x,i,j+1,k) ,subarray(e1y,i,j+1,k) , subarray(e1z,i,j+1,k) ,
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subarray(e2x,i+1,j,k) ,subarray(e2y,i+1,j,k) , subarray(e2z,i+1,j,k),
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subarray(e3x,i+1,j+1,k) ,subarray(e3y,i+1,j+1,k) , subarray(e3z,i+1,j+1,k) )
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######
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## --------
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# no | node | e1 | e2 | e3
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# 001 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k
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ind1 = sub2ind(me1,hstack3(ii,jj,kk+1))
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ind2 = sub2ind(me2,hstack3(ii,jj,kk+1)) + ne1
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ind3 = sub2ind(me3,hstack3(ii,jj,kk)) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P001 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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invT001 = inv3X3BlockDiagonal(subarray(e1x,i,j,k+1) ,subarray(e1y,i,j,k+1) , subarray(e1z,i,j,k+1) ,
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subarray(e2x,i,j,k+1) , subarray(e2y,i,j,k+1) , subarray(e2z,i,j,k+1) ,
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subarray(e3x,i,j,k) , subarray(e3y,i,j,k) , subarray(e3z,i,j,k) )
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## --------
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# no | node | e1 | e2 | e3
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# 101 | i+1,j ,k+1 | i ,j ,k+1 | i+1,j ,k+1 | i+1,j ,k+1
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ind1 = sub2ind(me1,hstack3(ii,jj,kk+1))
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ind2 = sub2ind(me2,hstack3(ii+1,jj,kk+1)) + ne1
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ind3 = sub2ind(me3,hstack3(ii+1,jj,kk)) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P101 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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invT101 = inv3X3BlockDiagonal(subarray(e1x,i,j,k+1), subarray(e1y,i,j,k+1), subarray(e1z,i,j,k+1) ,
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subarray(e2x,i+1,j,k+1), subarray(e2y,i+1,j,k+1) , subarray(e2z,i+1,j,k+1) ,
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subarray(e3x,i+1,j,k), subarray(e3y,i+1,j,k) , subarray(e3z,i+1,j,k) )
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## --------
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# no | node | e1 | e2 | e3
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# 011 | i ,j+1,k+1 | i ,j+1,k+1 | i ,j ,k+1 | i ,j+1,k+1
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ind1 = sub2ind(me1,hstack3(ii,jj+1,kk+1))
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ind2 = sub2ind(me2,hstack3(ii,jj,kk+1)) + ne1
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ind3 = sub2ind(me3,hstack3(ii,jj+1,kk)) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P011 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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invT011 = inv3X3BlockDiagonal(subarray(e1x,i,j+1,k+1) , subarray(e1y,i,j+1,k+1) , subarray(e1z,i,j+1,k+1) ,
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subarray(e2x,i,j,k+1) , subarray(e2y,i,j,k+1) , subarray(e2z,i,j,k+1) ,
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subarray(e3x,i,j+1,k) , subarray(e3y,i,j+1,k) , subarray(e3z,i,j+1,k) )
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## --------
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# no | node | e1 | e2 | e3
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# 111 | i+1,j+1,k+1 | i ,j+1,k+1 | i+1,j ,k+1 | i+1,j+1,k+1
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ind1 = sub2ind(me1,hstack3(ii,jj+1,kk+1))
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ind2 = sub2ind(me2,hstack3(ii+1,jj,kk+1)) + ne1
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ind3 = sub2ind(me3,hstack3(ii+1,jj+1,kk)) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P111 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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invT111 = inv3X3BlockDiagonal(subarray(e1x,i,j+1,k+1) , subarray(e1y,i,j+1,k+1) , subarray(e1z,i,j+1,k+1) ,
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subarray(e2x,i+1,j,k+1) , subarray(e2y,i+1,j,k+1) , subarray(e2z,i+1,j,k+1) ,
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subarray(e3x,i+1,j+1,k) , subarray(e3y,i+1,j+1,k) , subarray(e3z,i+1,j+1,k) )
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# Cell volume
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v = mkvc(getCellVolume(X,Y,Z)) #mkvc(getVolume(X,Y,Z))
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vsig = v*mkvc(sigma)
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v3 = vstack((vstack((vsig,vsig)),vsig))
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v3 = v3.flatten()
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V = sdiag(v3)
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A = P000.T*invT000.T*V*invT000*P000 + P001.T*invT001.T*V*invT001*P001 + P010.T*invT010.T*V*invT010*P010 + P011.T*invT011.T*V*invT011*P011 + P100.T*invT100.T*V*invT100*P100 + P101.T*invT101.T*V*invT101*P101 + P110.T*invT110.T*V*invT110*P110 + P111.T*invT111.T*V*invT111*P111
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A = 0.125*A
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return A
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if __name__ == '__main__':
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X,Y,Z = ndgrid(linspace(0,2,3),linspace(0,2,3),linspace(0,2,3))
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Z[2,2,2] = 2.5; Z[0,0,0] = -0.5
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X[2,2,2] = 2.5; X[0,0,0] = -0.5
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sig = ones([2,2,2])
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A = getEdgeInnerProduct(X,Y,Z,sig) |